An isolated system consists of a 1.5 kg mass moving in the presence of the following potential energy function: U open parenthes
es x close parentheses equals open parentheses 1 third straight J over straight m cubed close parentheses x cubed plus open parentheses 1 half straight J over straight m squared close parentheses x squared minus open parentheses 2 straight J over straight m close parentheses x What is the period (in s) of small amplitude oscillations of this system about its stable equilibrium point?
1 answer:
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Answer: see the graph attached (straight line, passing through the origin and positive slope).
Justification:
1) Kinetic energy and temperature are in direct proportion. That means:
i) Being kinetic energy y and temperature x: y α x
ii) That implies: y = kx,where k is the constant of proportionality.
iii) The graph is a line that passes through the origin and has positive slope k (k = y / x).
2) The proportional relationship between kinetic energy (KE) and temperature (T) is shown by the Boltzman law, which states:
Average KE = [3 / 2] KT, where K is Boltzman's constant, whose graph is of the form shown in the figure attached.
Justification:
1) Kinetic energy and temperature are in direct proportion. That means:
i) Being kinetic energy y and temperature x: y α x
ii) That implies: y = kx,where k is the constant of proportionality.
iii) The graph is a line that passes through the origin and has positive slope k (k = y / x).
2) The proportional relationship between kinetic energy (KE) and temperature (T) is shown by the Boltzman law, which states:
Average KE = [3 / 2] KT, where K is Boltzman's constant, whose graph is of the form shown in the figure attached.
D. distance = 23 m, displacement = + 1 m
Explanation:
Let's remind the difference between distance and displacement:
- distance is a scalar, and is the total length covered by an object, counting all the movements in any direction
- displacement is a vector connecting the starting point and the final point of a motion, so its magnitude is given by the length of this vector, and its direction is given by the direction of this vector.
In this case, the distance covered by Karen is given by the sum of all its movements:
The displacement instead is given by the difference between the final point (1.0 m in front of the starting line) and the starting point (the starting line, 0 m):
Answer:
0.76
Explanation:
we are given:
radius (r) =5.7 m
speed (s) = 1 revolution in 5.5 seconds
acceleration due to gravity (g) = 9.8 m/s^{2}
coefficient of friction (Uk) = ?
we can get the minimum coefficient of friction from the equation below
centrifugal force = frictional force
m x r x ω^{2} = Uk x m x g
r x ω^{2} = Uk x g
Uk =
where ω (angular velocity) =
= = 1.14
Uk = = 0.76